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Freely generated algebraic structure over a given signature
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature
Term_algebra
Branch of mathematics
context, algebra can also refer to other algebraic structures, like a Lie algebra or an associative algebra. The word algebra comes from the Arabic term الجبر
Algebra
Set with operations obeying given axioms
universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure
Algebraic_structure
Topics referred to by the same term
polynomial, or a series, a special case of a summand Term algebra, a freely generated algebraic structure Term logic, an approach to logic that began with Aristotle
Term
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Method to convey chess moves
threefold repetition rule). The term "algebraic notation" may be considered a misnomer, as the system is unrelated to algebra. Each square of the board is
Algebraic_notation_(chess)
Vector space equipped with a bilinear product
mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure
Algebra_over_a_field
Theory of algebraic structures in general
algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures
Universal_algebra
Islamic mathematician (c. 780 – c. 850)
equation), he has been described as the father or founder of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise
Al-Khwarizmi
Branch of mathematics
elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined
Abstract_algebra
Polynomial equation, generally univariate
multivariate polynomial equation over the rationals. For many authors, the term algebraic equation refers only to the univariate case, that is polynomial equations
Algebraic_equation
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until
History_of_algebra
Free object in the category of associative algebras
In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since
Free_algebra
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
Mathematical operation
triple product. The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the
Algebraic_operation
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Ring that is also a vector space or a module
article we will also use the term K-algebra to mean an associative algebra over K. A standard first example of a K-algebra is a ring of square matrices
Associative_algebra
Algebraic concept in measure theory, also referred to as an algebra of sets
Similarly the term "algebra over X {\displaystyle X} " is used in the sense of a Boolean algebra and should not be confused with algebras over fields or
Field_of_sets
Algebraic structure used in analysis
In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket
Lie_algebra
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Concept in universal algebra in mathematics
accordance with the custom to allow nullary terms and nullary term operations in universal algebra. Typically, publications studying clones as abstract clones
Clone_(algebra)
Branch of algebra that studies commutative rings
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both
Commutative_algebra
sentential logic, perceived as a term algebra with a consequence operation on its universe, the largest congruence on the algebra that is compatible with the
Leibniz_operator
Type of abstract object
of a function Domain theory Interpretation (logic) Quantifier (logic) Term algebra Universe (mathematics) Corcoran, John. Universe of discourse. Cambridge
Domain_of_discourse
System which describes the computational effects of computer programs
by the label of the memory region in which the cell resides). The term "algebraic effect" follows from the type system. Effect systems may be used to
Effect_system
optimization technique for rapidly locating the free variables in a term algebra or in a lambda expression. Director strings were introduced by Kennaway
Director_string
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Branch of mathematics that studies algebraic structures
algebra in Wiktionary, the free dictionary. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures
List of abstract algebra topics
List_of_abstract_algebra_topics
Concept in logic
Leeuwen (ed.). Algebraic Specification. Handbook of Theoretical Computer Science. Vol. B. Elsevier. pp. 675–788., here: p. 682. From a term algebra point of
Substitution_(logic)
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
Algebraic structure where all polynomials have roots
field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraically closed if
Algebraically_closed_field
Algebra in algebraic topology
In algebraic topology, a Steenrod algebra was defined by Henri Cartan (1955) to be the algebra of stable cohomology operations for mod p {\displaystyle
Steenrod_algebra
Universal construction in multilinear algebra
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any order) with multiplication being
Tensor_algebra
Topological complex vector space
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties
C*-algebra
Algebraic construct of interest in theoretical physics
mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include
Quantum_group
Branch of functional analysis
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with
Operator_algebra
Computational problem with high complexity
second-order theory with two successors (see S2S) the first-order theory of any term algebra in a signature containing at least one binary function symbol finite
Nonelementary_problem
System of equations in mathematics
a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is
Differential-algebraic system of equations
Differential-algebraic_system_of_equations
Mathematical expression using basic operations
mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers), variables, and the basic algebraic operations:
Algebraic_expression
Algebraic structure with a binary operation
In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with
Magma_(algebra)
Components of a mathematical or logical formula
important in, for example, term rewriting. Given a signature for the function symbols, the set of all terms forms the free term algebra. The set of all ground
Term_(logic)
mathematics, an affine Hecke algebra is the algebra associated to an affine Weyl group, and can be used to prove Macdonald's constant term conjecture for Macdonald
Affine_Hecke_algebra
Scientific area at the interface between computer science and mathematics
applications that perform symbolic calculations are called computer algebra systems, with the term system alluding to the complexity of the main applications that
Computer_algebra
Branch of mathematical statistics
Algebraic statistics is a branch of mathematical statistics that focuses on the use of algebraic, geometric, and combinatorial methods in statistics. While
Algebraic_statistics
Concept in mathematics
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal
Universal_enveloping_algebra
example below) which gives the valid constants and operations of the term algebra. The axiomatization (Axioms in the example below) which gives the semantics
Algebraic_Petri_net
9th-century Arabic work on algebra
algebra, and the first to teach algebra for its own sake. It also introduced the fundamental concept of "reduction" and "balancing" (which the term al-jabr
Al-Jabr
Reasoning about equations with free variables
and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics
Algebraic_logic
place-value system to include decimal fractions, the systematised study of algebra and advances in geometry and trigonometry. The medieval Islamic world underwent
Mathematics in the medieval Islamic world
Mathematics_in_the_medieval_Islamic_world
Replacing subterm in a formula with another term
objects are sequences of symbols, the objects of a term rewriting system form a term algebra. A term can be visualized as a tree of symbols, the set of
Rewriting
Type of 2D conformal field theory
group (or supergroup), and its symmetry algebra is the affine Lie algebra built from the corresponding Lie algebra (or Lie superalgebra). By extension, the
Wess–Zumino–Witten_model
Algebraic structure
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more
Polynomial_ring
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
list of topics around Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective
List of Boolean algebra topics
List_of_Boolean_algebra_topics
mathematics, noncommutative topology is a term used for the relationship between topological and C*-algebraic concepts. The term has its origins in the Gelfand–Naimark
Noncommutative_topology
Type of mathematical expression
used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry. The word polynomial joins two
Polynomial
1969 non-fiction book by G. Spencer-Brown
Restricted Recursive Arithmetic (RRA). "Boundary algebra" is a Meguire (2011) term for the union of the primary algebra and the primary arithmetic. Laws of Form
Laws_of_Form
Sporadic simple group
In the area of modern algebra known as group theory, the baby monster group B (or, more simply, the baby monster) is a sporadic simple group of order
Baby_monster_group
algebras are Boolean algebras. This was proved by William McCune in 1997, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra"
Robbins_algebra
Mathematical representation in functional analysis
representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric
Gelfand_representation
Concept in mathematics
intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology. A one-dimensional formal
Formal_group_law
The term Cantor algebra is also occasionally used to mean the Boolean algebra of all clopen subsets of the Cantor set, or the Boolean algebra of Borel
Jónsson–Tarski_algebra
Construction in algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)
Hopf_algebra
Study of polynomial equations
term "theory of equations" is mainly used in the context of the history of mathematics, to avoid confusion between old and new meanings of "algebra"
Theory_of_equations
In abstract algebra, the term associator is used in different ways as a measure of the non-associativity of an algebraic structure. Associators are commonly
Associator
term "Weil algebra" is also sometimes used to mean a finite-dimensional real local Artinian ring. In mathematics, the Weil algebra of a Lie algebra g
Weil_algebra
Class of mathematical sets
sequence of sets is termed the Borel hierarchy. An important example, especially in the theory of probability, is the Borel algebra on the set of real
Borel_set
Algebraic structure used in logic
In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with
Heyting_algebra
Element of a unital algebra over the field of real numbers
mathematics, the hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex
Hypercomplex_number
Algebraic structure modeling logical operations
and theorems of Boolean algebra express the symmetry of the theory described by the duality principle. The term "Boolean algebra" honors George Boole (1815–1864)
Boolean_algebra_(structure)
Algebraic structure with addition, multiplication, and division
operations on rational numbers do. Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
In mathematics, a type of algebra
a Lie algebra g {\displaystyle {\mathfrak {g}}} is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra of the Lie
Solvable_Lie_algebra
American mathematician (Jon Peter May; born 1939)
September 16, 1939) is an American mathematician working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects
J._Peter_May
Property of operations
referential transparency). The term was introduced by American mathematician Benjamin Peirce in 1870 in the context of elements of algebras that remain invariant
Idempotence
*-algebra of bounded operators on a Hilbert space
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology
Von_Neumann_algebra
supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains
Supersymmetry_algebra
Algebraic ring without a multiplicative identity
In abstract algebra, a rng (pronounced "rung" /rʌŋ/) or non-unital ring or pseudo-ring is an alternative name for a ring that does not assume the existence
Rng_(algebra)
operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are
Jordan_operator_algebra
Homomorphism from an initial algebra into another algebra
homomorphism from an initial algebra into some other algebra. Catamorphisms provide generalizations of folds of lists to arbitrary algebraic data types, which can
Catamorphism
Area of combinatorics
conversely, applies combinatorial techniques to problems in algebra. The term "algebraic combinatorics" was introduced in the late 1970s. Through the
Algebraic_combinatorics
mathematics, in particular abstract algebra and topology, a homotopy Lie algebra (or L ∞ {\displaystyle L_{\infty }} -algebra) is a generalisation of the concept
Homotopy_Lie_algebra
Number in {..., –2, –1, 0, 1, 2, ...}
numbers. In algebraic number theory, integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In
Integer
Algebra term in mathematics
In mathematics, a double affine Hecke algebra, or Cherednik algebra, is an algebra containing the Hecke algebra of an affine Weyl group, given as the
Double_affine_Hecke_algebra
Formal grammar
form A → t, with A ∈ N, and t ∈ TΣ(N), where TΣ(N) is the associated term algebra, i.e. the set of all trees composed from symbols in Σ ∪ N according to
Regular_tree_grammar
Deformation of the group algebra of a Coxeter group
algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group. The Hecke algebra can
Iwahori–Hecke_algebra
Four-dimensional number system
Lipschitz' algebras "hyperquaternions". The term "hyperquaternion" designates nowadays both the tensor product of n {\displaystyle n} quaternion algebras H ⊗
Quaternion
Algebra combining both supersymmetry and conformal symmetry
algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. In two dimensions, the superconformal algebra is
Superconformal_algebra
Simplification technique in mathematical logic
arithmetic, Skolem arithmetic, algebraically closed fields, real closed fields, atomless Boolean algebras, term algebras, dense linear orders, abelian
Quantifier_elimination
Index of articles associated with the same name
The term center or centre is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements
Center_(algebra)
Description of non-logical symbols
symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures
Signature_(logic)
Left adjoint to a forgetful functor to sets
basic concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only
Free_object
mathematics, the term Beurling algebra is used for various different algebras introduced by Arne Beurling (1949). Usually it is an algebra of periodic functions
Beurling_algebra
Study of the properties of codes and their fitness
needed] The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then
Coding_theory
Branch of mathematics
Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument
Multilinear_algebra
postulate. Abstract algebra The part of algebra devoted to the study of algebraic structures in themselves. Occasionally named modern algebra in course titles
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Symmetric bilinear form in mathematics
bilinear form that plays a basic role in the theories of Lie groups and Lie algebras. Cartan's criteria (criterion of solvability and criterion of semisimplicity)
Killing_form
Topics referred to by the same term
geometric algebra is a specific algebraic structure. The term is also used as a blanket term for the theory of geometric algebras. Geometric algebra may also
Geometric algebra (disambiguation)
Geometric_algebra_(disambiguation)
In functional analysis, the Calkin algebra, named after John Williams Calkin, is the quotient of B(H), the ring of bounded linear operators on a separable
Calkin_algebra
Topics referred to by the same term
Topics referred to by the same term
Product
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
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